Approach Geometry Questions from the Right (tri)Angle
(This is one of a series of GMAT tips that we offer on our blog.)
As the writers of the GMAT create difficult quantitative questions, one favorite technique is to require test-takers to use skills that would not, on the surface, seem relevant. As examinees struggle to find a foothold on the question with the tools that seem more obvious by comparison, they lose time, make calculation errors, and suffer not only from an incorrect answer but also from a decreased level of confidence that carries on to future questions.
One such seemingly-irrelevant skill that appears on a majority of geometry-based questions is the right triangle, a shape for which you should train yourself to look whenever a geometry question appears. Every shape that the GMAT tests could contain a right triangle:
- The area of a non-right triangle is created by taking a perpendicular line from the base to the angle opposite it; this process divides the original triangle in to two right triangles.
- The diagonal of a square or rectangle is a right triangle.
- The area of a parallelogram or trapezoid is found by taking a perpendicular line between the bases; doing so can create a right triangle.
- Even in a circle, connecting the diameter to a point on the edge of the circle, using two chords to do so, will create a right triangle with the diameter as the hypotenuse.
- In 3-D figures, the longest difference between two points on the item is always a hypotenuse of a right triangle that must be drawn in space.
By training yourself to look for opportunities to use your knowledge of right triangles, even if it doesn’t appear to be the obvious skill to apply, you will save time and build confidence on most geometry-based questions.
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